A DESIGN FOR MARKET SOCIALISM By John Roemer May 2017 COWLES FOUNDATION DISCUSSION PAPER NO. 2090 COWLES FOUNDATION FOR RESEARCH IN ECONOMICS YALE UNIVERSITY Box 208281 New Haven, Connecticut 06520-8281 http://cowles.yale.edu/ 1 “A Design for Market Socialism” by John E. Roemer* Abstract. Socialism is conceptualized as a society in which individuals cooperate, distinguished from capitalism, characterized as involving ubiquitous economic competition. Here, I embed a formal model of cooperation in an Arrow-Debreu model, using the Kantian optimization protocol, and define a Walras-Kant equilibrium, in which firms maximize profits, consumers choose demands for commodities in the usual utility- maximizing fashion, and the state rents capital to firms. The labor-supply decision of workers, however, is arrived at using the cooperative protocol. Incomes are redistributed through a flat income tax. Walras-Kant equilibria, with any desired degree of income equality exist, are decentralizable, and are Pareto efficient. Key words: market socialism, general equilibrium, first welfare theorem, cooperation, Kantian optimization JEL codes: D50, D59, D63, P20 * Yale University, Department of Political Science. I thank Joaquim Silvestre, Burak Ünveren and Andreu Mas-Colell for comments and advice. This paper is dedicated to the memory of G.A. Cohen. 1 In my view, the principal problem that faces the socialist ideal is that we do not know how to design the machinery that would make it run. Our problem is not, primarily, human selfishness, but our lack of a suitable organizational technology: our problem is a problem of design. It may be an insoluble design problem, and it is a design problem that is undoubtedly exacerbated by our selfish propensities, but a design problem, so I think, is what we’ve got. (G.A. Cohen, 2009) 1. The design problem So wrote the philosopher G.A. Cohen in his last work, published posthumously. To explicate the problem Cohen was describing: we know that, if economic agents are self- regarding, and a suitable set of conditions hold, then decentralized optimization in a capitalist economy by individuals and firms engenders, at equilibrium, a Pareto efficient allocation (the first theorem of welfare economics). Suppose, now, that individuals wish to cooperate with each other, wish to behave in a solidaristic manner. In a word, they possess a ‘socialist ethos.’ Is there an economic mechanism that can decentralize decision-making in a market economy, harnessing that cooperative impulse, to deliver a Pareto efficient and equitable allocation? This is the Cohen design problem. In this article, I propose such a design. Cooperation is modeled as Kantian optimization in the labor-supply decisions of workers. Kantian optimization as a method of decentralizing cooperative behavior has been studied in Roemer [2010, 2015, in press]. What’s new about the present analysis is inserting Kantian optimization into an Arrow- Debreu economy, in which firms are privately owned and maximize profits in the traditional manner. The models presented can be thought of as describing a blueprint for market socialism. The market-socialist tradition proposes to replace central planning with markets – or, in the design of Oscar Lange and Fred Taylor (1938)—with pseudo markets. In all models of market socialism heretofore, firms have been owned by the state, or by collectives of workers, or by other institutions, rather than by private citizens. James Meade’s (1962) model of a ‘property-owning democracy’ achieved a degree of May 31, 2017 2 equalization of capital income by providing incentives to distribute estates in a diffuse manner; he advocated both comprehensive education and a eugenics policy as instruments for equalizing labor incomes. In my earlier proposal (Roemer [1994]), all young adults were issued a property right to dividends in the nation’s publicly owned firms; firm shares could be traded on a special stock market, but could not be liquidated for cash. The intention was, again, to equalize (roughly) the distribution of capital income. In Giacomo Corneo’s (in press) recent contribution, firms are again state- owned by a ‘federal shareholder,’ profits escheat to the Treasury, and are used to finance demogrants to citizens and investment. Market-socialist models to date have not modeled cooperation or solidarity among citizens although these features are at the heart of the socialist ideal. Despite the importance of cooperation to the socialist vision, existing models present no explicit conception of how people would behave differently (cooperatively) in a socialist society from how they behave (autarchically) in a capitalist economy. In market-socialist models heretofore, agents are presumed to optimize in the same way that Arrow-Debreu agents optimize, maximizing a self-regarding preference order subject to constraints. One might suppose that socialist citizens would possess preferences with an altruistic element in them. However, I have not seen any market-socialist models with this property – and in any case, if an agent is small in the economy, it is unclear whether his having a preference order with an altruistic character would produce equilibria any different from one in which agents are entirely self-regarding. (See Dufwenberg et al [2011].) After all, if an agent is small, what difference would his altruistic contribution make, and would this small contribution outweigh the personal cost he sustains by making it? The preferences of agents are standard and self-regarding in my proposal. Income taxation is the redistributive mechanism here. The key observation is that Kantian (as opposed to Nash) optimization in the labor-supply decision nullifies the usual deadweight loss incurred with income taxation. Any degree of post-fisc income equality can be achieved without sacrificing Pareto efficiency. The economic mechanism is decentralized, efficient, and as equal as citizens choose it to be, through a presumably democratic choice of the tax rate. May 31, 2017 3 Combining an Arrow-Debreu structure with additive Kantian optimization offers a solution to Cohen’s design problem. In section 2, I briefly review the definition of Kantian optimization, and define a Walras-Kant (W-K) equilibrium with taxation. In section 3, I present the welfare theorem: under general conditions, Walras-Kant equilibria are Pareto efficient, at any tax rate. Section 4 presents an example. Section 5 proves the existence of W-K equilibria at almost any tax rate. Section 6 discusses the psychology of Kantian optimization and concludes. 2. The proposed design1 A. Kantian equilibrium in games I begin by reminding the reader of the definition of Kantian equilibrium in a game (Roemer [2009, 2015]). Consider a game with n agents, each of whom plays a strategy chosen from an interval of real numbers. Denote the payoff function of player i by . Definition 2.1 An additive Kantian equilibrium of the game is a strategy profile such that no player would like to add any scalar to all strategies; that is: . (2.1) Mathematically, additive Kantian equilibrium has a similar structure to Nash equilibrium. The difference is in the counterfactuals the agents contemplate when considering a deviation from a given strategy profile. In Nash equilibrium each agent imagines changing her strategy while all other agents stand pat. In Kantian equilibrium, each agent imagines changing all strategies in a symmetric manner. In Nash optimization, agents imagine choosing their best option from different sets of counterfactual strategy profiles; in Kantian optimization, all agents imagine choosing their best option from the 1 Notational conventions: Scalar variables are italic, vectors and matrices are boldface roman. If is a vector, then . Denote the partial derivative of any real-valued function f by . May 31, 2017 4 same set of counterfactual profiles. Choosing their favorite strategy profile from a common set of counterfactuals is the mathematical form that solidarity/cooperation takes. Definition 2.3 A game is (strictly) monotone increasing if for each i, is (strictly) increasing in the strategies of all other players . A game is (strictly) monotone decreasing if for each i, is (strictly) decreasing in the strategies of all other players. Monotone increasing games are ones with positive externalities – an example being where the strategies are contributions to a public good. Monotone decreasing games are ones with negative externalities – an example being the tragedy of the commons. Any additive Kantian equilibrium of a strictly monotone game is Pareto efficient in the game. Thus, Kantian optimization decentralizes an efficient solution of games with positive and negative externalities. It solves free-rider problems. This provides a justification for viewing Kantian optimization as a model of cooperative behavior. B. A labor-supply game (i) The economic environment I begin by defining an economic environment. There are two produced private goods and a homogeneous kind of labor, measured in efficiency units. There are two firms, each of which produces one of the goods from inputs of labor and capital, using production functions G and H respectively, which map . Worker i is endowed with units of labor in efficiency units, and receives a profit share from Firm l , for . The state owns fractions of firm , and is endowed with units of the capital good. Good 1 is used both for consumption and capital, and Good 2 is a pure consumption good. The state uses its capital to finance investment in the two firms, and the private agents spend their incomes on consumption of the two goods. Private agent i has preferences over the two consumption goods and labor expended (in efficiency units) May 31, 2017 5 represented by a utility function . All activity takes place in a single period. For purposes of expositional simplicity, I have specified an environment with two produced commodities and two firms. All the results below generalize to any number of firms producing any number of commodities, in the obvious manner. Firms are traditional – they are price-takers and demand capital and labor and supply commodities to maximize profits.